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-rw-r--r--entries/markusde/collatz/collatz.pdfbin0 -> 87475 bytes
-rw-r--r--entries/markusde/collatz/collatz.pngbin0 -> 27596 bytes
-rw-r--r--entries/markusde/collatz/collatz.tex21
-rw-r--r--people.json11
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diff --git a/entries/markusde/collatz/collatz.tex b/entries/markusde/collatz/collatz.tex
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+\documentclass[12pt]{article}
+\usepackage[landscape]{geometry}
+\usepackage{amsmath}
+\usepackage{amsfonts}
+\usepackage{amsthm}
+\renewcommand{\phi}{\varphi}
+\begin{document}
+
+\noindent The least fixed point of
+\begin{align*}
+ h & : (\mathbb{N}_\bot \to \mathbb{Z}_\bot) \to (\mathbb{N}_\bot \to \mathbb{Z}_\bot) \\
+ h(F)(n) & =
+ \begin{cases}
+ 1 & n = 1 \\
+ (\phi^{n/2} + (-\phi)^{-n/2})\, F_{n/2} & n \textrm{ is even} \\
+ \sqrt[3]{\frac{\phi^{3n+1}-\phi F_{3n+1}}{10} + \frac{\sqrt{25 \phi^{3n+1} - 25\phi F_{3n+1} - 20}}{50}} + \sqrt[3]{\frac{\phi^{3n+1}-\phi F_{3n+1}}{10} - \frac{\sqrt{25 \phi^{3n+1} - 25\phi F_{3n+1} - 20}}{50}} & \textrm{otherwise} \\
+ \end{cases}
+\end{align*}
+is the Fibonacci sequence if and only if the Collatz conjecture is true.
+
+\end{document}
diff --git a/people.json b/people.json
index 2eff422..112f116 100644
--- a/people.json
+++ b/people.json
@@ -329,5 +329,16 @@
"link": "./entries/dewert99/fib.rs"
}
]
+ },
+ {
+ "github": "markusdemedeiros",
+ "name": "Markus de Medeiros",
+ "title": "BSc Student, UBC",
+ "entries": [
+ {
+ "name": "collatz",
+ "link": "./entries/markusde/collatz/collatz.png"
+ }
+ ]
}
]